Systems and methods for cyclostationary feature elimination

ABSTRACT

Systems (400) and methods for removing dither introduced into a transmitted RF signal. The method comprising: receiving, by a receiver, the transmitted RF signal; converting, by the receiver, the transmitted RF signal into a discrete-time IF signal comprising a sequence of samples, where at least a first sample of said samples has a first sample duration different than a second sample duration of at least a second sample of said samples; and performing operations by a sub-sample dither removal device of the receiver to modify a sample timing of the discrete-time IF signal by decreasing or increasing the first sample duration of the first sample using a digital signal processing technique in a digital domain.

FIELD

This document relates generally to communication systems. Moreparticularly, this document relates to implementing systems and methodsfor cyclostationary feature elimination.

BACKGROUND

There are many transmit modulation schemes known in the art. Thesetransmit modulation schemes include M-ary Phase Shift Keying (“MPSK”),M-ary Quadrature Amplitude Modulation (“MQAM”), M-ary Frequency ShiftKeying (“FSK”), Continuous Phase Modulation (“CPM”), and OrthogonalFrequency Division Multiplexing (“OFDM”). The listed transmit modulationschemes have inherent cyclostationary properties that can be used todetect the transmitted waveforms. A chip rate detector is often used todetect the transmitted waveforms.

SUMMARY

The present disclosure concerns implementing systems and methods forremoving dither introduced into a transmitted RF signal. The methodscomprise: receiving, by a receiver, the transmitted RF signal; andconverting, by the receiver, the transmitted RF signal into adiscrete-time IF signal comprising a sequence of samples. At least afirst sample of the samples has a first sample duration different than asecond sample duration of at least a second sample of said samples. Asub-sample dither removal device of the receiver performs operations tomodify a sample timing of the discrete-time IF signal by decreasing orincreasing the first sample duration of the first sample using a digitalsignal processing technique. The digital signal processing techniqueincludes, but is not limited to, a polyphase resampling filtertechnique, a sample dropping/repeating technique, or a Farrow filtertechnique that adds or drops a plurality of samples from thediscrete-time IF signal.

In some scenarios, a time advance equal to one sample duration isremoved from the discrete-time IF signal at the sub-sample ditherremoval device by repeating a sample in a sequence of output samples. Atime advance equal to an amount of a sample duration is removed from thediscrete-time IF signal at the sub-sample dither removal device byintroducing a time retardation equal to the amount of the sampleduration into the discrete-time IF signal. A time retardation equal toan amount of a sample duration is removed from the discrete-time IFsignal at the sub-sample dither removal device by introducing a timeadvancement equal to the amount of the sample duration into thediscrete-time IF signal.

In those or other scenarios, the first sample duration of the firstsample is longer than the second sample duration of the second sample.The first sample duration is decreased by a first incremental amount ofa sample duration by outputting results only from a first select one ofa plurality of polyphase filter banks from the sub-sample dither removaldevice. The results from all unselected ones of the poyphase filterbanks are discarded or not computed. The duration of at least one thirdsample of the sequence is decreased by a second incremental amount ofthe sample duration by outputting results only from a second select oneof the plurality of polyphase filter banks from the sub-sample ditherremoval device.

In those or other scenarios, the first sample duration of the firstsample is shorter than the second sample duration of the second sample.The first sample duration is increased by a first incremental amount ofa sample duration by outputting only one result from a first select oneof a plurality of polyphase filter banks of the sub-sample ditherremoval device, immediately followed by at least one result from asecond different select one of the plurality of polyphase filter banks.The duration of at least one third sample of the sequence is increasedby a second incremental amount of the sample duration by outputting onlyone result from the first select one of a plurality of polyphase filterbanks of the sub-sample dither removal device, immediately followed byat least one result from a third different select one of the pluralityof polyphase filter banks.

DESCRIPTION OF THE DRAWINGS

The present solution will be described with reference to the followingdrawing figures, in which like numerals represent like items throughoutthe figures.

FIG. 1 is an illustrative graph showing the results of a conventionalspectral correlation function.

FIG. 2 is an illustrative graph showing the results of a chip ratedetector.

FIG. 3 provides illustrative graphs showing a waveform before and afterapplication of sub-sample dithering in accordance with the presentsolution.

FIG. 4 is an illustration of an illustrative communications systemimplementing the present solution.

FIG. 5 is an illustration of an illustrative architecture for thetransmitter of FIG. 4.

FIG. 6 is an illustration of an illustrative architecture for thesub-sample dithering processing device shown in FIG. 5.

FIG. 7 is an illustration that is useful for understanding polyphaseresampling filter operations performed by the sub-sample ditheringprocessing device shown in FIG. 6.

FIG. 8 is an illustration of an illustrative architecture for apolyphase filter.

FIG. 9 is an illustration that is useful for understanding aconventional 4:1 interpolation with four input samples.

FIG. 10 is an illustration that is useful for understanding aconventional 1:1 interpolation: decimation process with four inputsamples.

FIG. 11 is an illustration showing an illustrative time advancement in asequence of samples and a time retardation in a sequence of samples.

FIGS. 12A-12D (collectively referred to as “FIG. 12”) provideillustrations that are useful for understanding operations of thesub-sample dithering processing device shown in FIG. 6 for introducing atime advance in a sequence of samples.

FIGS. 13A-13C (collectively referred to as “FIG. 13”) provideillustrations that are useful for understanding operations of thesub-sample dithering processing device shown in FIG. 6 for introducing atime retard or delay in a sequence of samples.

FIG. 14 is an illustration of an illustrative architecture for thereceiver of FIG. 4.

FIG. 15 is an illustration of an illustrative architecture for thesub-sample dithering processing device shown in FIG. 13.

FIG. 16 is an illustration that is useful for understanding polyphasedesampling filter operations performed by the sub-sample ditheringprocessing device shown in FIG. 15.

FIG. 17 is an illustration of an illustrative polyphase filter employedon a receive side.

FIG. 18 is an illustration that is useful for understanding theoperations of the polyphase filter shown in FIG. 17.

FIGS. 19A-19D (collectively referred to as “FIG. 19”) provideillustrations that are useful for understanding how time advancementsare removed from a signal at the receiver of FIG. 4.

FIGS. 20A-20C (collectively referred to as “FIG. 20”) provideillustrations that are useful for understanding how time retardationsare removed from a signal at the receiver of FIG. 4.

FIG. 21, there is provided a graph useful for understanding operationsof the present solution.

FIG. 22 is a graph showing an improved performance of a communicationssystem implementing the present solution as compared to that ofconventional communications systems.

DETAILED DESCRIPTION

It will be readily understood that the components of the embodiments asgenerally described herein and illustrated in the appended figures couldbe arranged and designed in a wide variety of different configurations.Thus, the following more detailed description of various embodiments, asrepresented in the figures, is not intended to limit the scope of thepresent disclosure, but is merely representative of various embodiments.While the various aspects of the embodiments are presented in drawings,the drawings are not necessarily drawn to scale unless specificallyindicated.

The present invention may be embodied in other specific forms withoutdeparting from its spirit or essential characteristics. The describedembodiments are to be considered in all respects only as illustrativeand not restrictive. The scope of the invention is, therefore, indicatedby the appended claims rather than by this detailed description. Allchanges which come within the meaning and range of equivalency of theclaims are to be embraced within their scope.

Reference throughout this specification to features, advantages, orsimilar language does not imply that all of the features and advantagesthat may be realized with the present invention should be or are in anysingle embodiment of the invention. Rather, language referring to thefeatures and advantages is understood to mean that a specific feature,advantage, or characteristic described in connection with an embodimentis included in at least one embodiment of the present invention. Thus,discussions of the features and advantages, and similar language,throughout the specification may, but do not necessarily, refer to thesame embodiment.

Furthermore, the described features, advantages and characteristics ofthe invention may be combined in any suitable manner in one or moreembodiments. One skilled in the relevant art will recognize, in light ofthe description herein, that the invention can be practiced without oneor more of the specific features or advantages of a particularembodiment. In other instances, additional features and advantages maybe recognized in certain embodiments that may not be present in allembodiments of the invention.

As used in this document, the singular form “a”, “an”, and “the” includeplural references unless the context clearly dictates otherwise. Unlessdefined otherwise, all technical and scientific terms used herein havethe same meanings as commonly understood by one of ordinary skill in theart. As used in this document, the term “comprising” means “including,but not limited to”.

Techniques are desired which can reduce the inherent cyclostationaryproperties of transmitted waveforms in order to reduce their probabilityof detection making them Low Probability of Detection (“LPD”) and LowProbability of Intercept (“LPI”) without affecting the demodulationperformance of the waveforms. The present solution provides such atechnique.

There are several conventional algorithms used in cyclo stationaryfeature detection. Detection of cyclo stationary features allows areceiving device to gain knowledge of when a transmitter (e.g., an UAV)is transmitting a signal (e.g., video). When such knowledge is gained, anefarious party may locate the transmitter and destroy it. This is notdesirable in many applications, especially military applications.

One such conventional method is a frequency domain method known as theSpectral Correlation Function (“SCF”). The SCF method uses a FastFourier Transform (“FFT”) of the incoming signal and thenauto-correlates the signal with itself for every combination of an FFTbin offset. FIG. 1 provides a graph showing illustrative results fromperforming the SCF method. The graph of FIG. 1 shows the frequencyoffset from zero. If BPSK modulation is employed without any frequencyoffset from bin zero, then there would be only one BPSK modulation tonein the center of the graph. But, because a slight frequency offset isemployed, four BPSK modulation tones appear in the center of the array.One dimension represents an FFT size (e.g., 4096), and a seconddimension represents the frequency offset. The cyclostationary featuresare the smaller tones on the sides of each BPSK modulation tone.

Another such method is a time domain detection method employed by chiprate detectors. For this analysis, the FFT of the result illustrates theposition of the cyclo stationary features. At the output of the FFT,cyclo stationary features exist in bins. The bins are exactly in theposition of the symbol rate. Second-order time domain cyclo stationaryproperties are computed as the input signal squared or input signaltimes the conjugate of itself x*x or x*x* to obtain power values.Fourth-order time domain cyclo stationary properties are computed asx*x*x*x or x*x**x*x*. The output of a chip rate detector implementing afourth-order time domain algorithm is shown in FIG. 2. Twocyclostationary features exists in FIG. 2.

Varying the symbol rate can reduce or eliminate the cyclostationaryfeatures. The term “symbol rate” or “baud rate”, as used herein, referto the number of symbols per second measured in baud (Bd). The plotsshown in FIGS. 1-2 require a lot of averaging over long periods of timefor the cyclostationary features to appear. Varying the symbol rate inthese conventional techniques degrades the averaging to the point ofinhibiting detection.

In the present solution, the symbol rate is varied throughout a singleburst transmission using polyphase resampling filter operations tomodify the symbol timing. This technique provides a communicationsdevice with a small degradation in Bit Error Rate (“BER”) performance,as displayed in FIG. 22. FIG. 22 shows that there is only a 0.25 dBdegradation of the BER in a communications system implementing thepresent solution.

A polyphase resampling filter operations provide a computationaloptimization of a standard interpolate-filter-decimate algorithm. Withinterpolation, zero's are added to the incoming digital stream ofsamples. Rather than perform (wasted) multiplication of zero's times thesignal, a reduced set of coefficients are created (in a single ‘bank’ ofcoefficients) to be multiplied by the non-zero samples. In a set ofpolyphase resample coefficient banks, each combination of coefficientsis available. By selecting a change in a filter bank, the systemadvances or retards the signal timing via sample duration modifications.FIG. 3 shows the waveform before and after application of sub-sampledithering in accordance with the present solution.

Conventional analog methods utilize sample-and-hold circuits whichrequire higher overall sample rates at both the receiver and thetransmitter. The present solution allows radios to process samples atthe modulation chip rate while adding sub-sample dithering, thusreducing power and complexity of the radio system. The sample processinginvolves performing operations by a sub-sample dithering processingdevice of the transmitter to modify a sample timing of the discrete-timeIF signal by decreasing or increasing a duration of at least one firstsample of the sequence using a digital signal processing technique inthe digital domain. The digital signal processing technique includes,but is not limited to, a polyphase resampling filter technique, a sampledropping/repeating technique, or a Farrow filter technique. Polyphaseresampling filters, sample dropping/repeating element, and Farrowfilters are known in the art. However, such filters and elements areconventionally used at the receiver side, and not at the transmitterside as is done in the present solution. The sample dropping/repeatingtechnique and Farrow filter technique are more complex and lessefficient as compared to the polyphase filter implementations. As such,the present solution will be described herein in relation to thepolyphase filter implementations. However, the present solution is notlimited in this regard.

Illustrative Communications Architecture

Referring now to FIG. 4, there is provided an illustration of anillustrative communications system 400. Communications system 400 isgenerally configured to allow communications amongst a plurality ofradios 402 with a low probability of detection. In this regard, thecommunications system 400 comprises a transmitter 404 and a receiver406. Transmitter 404 is configured to generate a discrete-time IFsignal, convert the discrete-time IF signal into an analog signal, andcommunicate the analog signal to the receiver 406 over a communicationslink 408. Prior to being transmitted, the sample timing of thediscrete-time IF signal is modified in accordance with a novelsub-sample dithering scheme, which is described in detail below. At thereceiver 406, an inverse of the sub-sample dithering scheme is performedto recover the original discrete-time IF signal.

Referring now to FIG. 5, there is provided a more detailed block diagramof the transmitter 404. Transmitter 404 has been selected to illustratethe introduction of symbol timing modifications into the transmit side.In this regard, it should be understood that the transmitter 404comprises a sub-sample dithering processing device 504, aDigital-to-Analog Converter (“DAC”) 506, an IF to RF converter 508, andan antenna 510.

The sub-sample dithering processing device 504 is configured to receivea discrete-time IF signal 502 (i.e., a sequence of samples), process thesame to selectively introduce time advances and/or delays in a sequenceof samples, and provide the sequence of samples with the time advancesand/or time delays to the DAC 506. An illustrative architecture of thesub-sample dithering processing device 504 is provided in FIG. 6. FIG. 6will be discussed below.

The DAC 506 is configured to receive the sequence of samples from device504, convert the same into an analog signal, and communicate the analogsignal to the IF to RF converter 508. DACs are well known in the art,and therefore will not be described herein. Any known or to be known DACcan be used herein without limitation.

IF to RF converter 508 is configured to translate in frequency arelatively low-frequency IF signal up to a transmitted RF signal.Apparatus and methods for performing IF to RF conversions are well knownto persons having ordinary skill in the art of RF transmitter design,and therefore will not be described herein. IF to RF converter 508 isconfigured to communicate RF signals to antenna 510 for broadcast to adesired receiver.

Referring now to FIG. 6, there is provided a detailed block diagram ofan illustrative architecture for the sub-sample dithering processingdevice 504. Device 504 may include more or less components than thoseshown in FIG. 6. However, the components shown are sufficient todisclose an illustrative embodiment implementing the present solution.The hardware architecture of FIG. 6 represents one embodiment of arepresentative sub-sample dithering processing device configured tofacilitate cyclo stationary feature elimination. As such, the device 504of FIG. 5 implements at least a portion of a method for selectivelyintroducing time advances and/or delays in a sequence of samples inaccordance with the present solution.

Some or all components of the device 504 can be implemented as hardware,software and/or a combination of hardware and software. The hardwareincludes, but is not limited to, one or more electronic circuits. Theelectronic circuits can include, but are not limited to, passivecomponents (e.g., resistors and capacitors) and/or active components(e.g., amplifiers and/or microprocessors). The passive and/or activecomponents can be adapted to, arranged to and/or programmed to performone or more of the methodologies, procedures, or functions describedherein.

As shown in FIG. 6, the device 504 comprises an input port 602, aprocessing unit 606, an output port 604, a system bus 610, a randomnumber generator 616, a memory 612 connected to and accessible by otherportions of device 504 through system bus 610, and hardware entities 614connected to system bus 610.

At least some of the hardware entities 614 perform actions involvingaccess to and use of memory 612. Hardware entities 614 can include acomputer-readable storage medium 618 on which is stored one or more setsof instructions 620 (e.g., software code) configured to implement one ormore of the methodologies, procedures, or functions described herein.The instructions 620 can also reside, completely or at least partially,within the memory 612 and/or within the processing unit 606 duringexecution thereof by the device 504. The memory 612 and the processingunit 606 also can constitute machine-readable media. The term“machine-readable media”, as used here, refers to a single medium ormultiple media that store the one or more sets of instructions 620. Theterm “machine-readable media”, as used here, also refers to any mediumthat is capable of storing, encoding or carrying a set of instructions620 for execution by the device 504 and that cause the device 504 toperform any one or more of the methodologies of the present disclosure.

Referring now to FIGS. 7-8, there are provided illustrations that areuseful for understanding the operations performed by the sub-sampledithering processing device 504. The operations include polyphaseresampling filter operations 704 for selectively introducing timeadvances or time retardations (or delays) in a sequence of samples X0,X1, X2, . . . , X11. The output of the polyphase resampling filteroperations 704 is referred to herein as a sequence of samples Z0, Z1,Z2, . . . , Z11. Notably, the polyphase resampling filter operations 704outputs the same number of samples as it receives, i.e., there is a 1 to1 correspondence between input samples and output samples. Although thesequence of samples is shown in FIG. 7 as comprising twelve samples, thepresent solution is not limited in this regard. The sequence of samplescan comprise any number of samples in accordance with a givenapplication. Also, the sequence of samples X0, X1, X2, . . . , X11 canbe an entire sequence of samples or any part of a larger sequence ofsamples.

The duration of each time advance and/or time delay may be randomlyselected using the random number generator 616 of FIG. 6 and a pluralityof polyphase filter banks 802, 804, 806, 808. In some scenarios, 128polyphase filter banks are provided, each with 12 coefficients, so thattime advances and delays which are multiples of 1/128 of a sampleduration can be chosen. The present solution is not limited in thisregard.

Polyphase filter banks are well known in the art, and therefore will notbe described herein in detail. Still, a brief discussion of howpolyphase filter banks have conventionally been used is now provided toassist in understanding the novel way in which polyphase filter banksare being used in the present solution.

Referring now to FIG. 9, there is provided an illustration that isuseful for understanding operations of a polyphase filter in a 4:1interpolation application. The polyphase filter is defined by thefollowing Mathematical Equation.

$Y_{n} = {\sum\limits_{k = 0}^{k = 16}{C_{k}X_{n - k}}}$where Y_(n) represents the output of the polyphase filter, C_(k)represents a polyphase filter coefficient and X_(n-k) represents aninput sample. The polyphase filter is designed to output four samplesfor every one sample input thereto. In this regard, the polyphase filtercomprises four polyphase filter banks 902, 904, 906, 908. Each filterbanks has four coefficients assigned thereto. More specifically, a firstpolyphase filter bank 902 has coefficients C0, C4, C8 and C12 assignedthereto. A second polyphase filter bank 904 has coefficients C1, C5, C9and C13 assigned thereto. A third polyphase filter bank 906 hascoefficients C2, C6, C10 and C14 assigned thereto. A fourth polyphasefilter bank 908 has coefficients C3, C7, C11 and C15 assigned thereto.

Operation of this polyphase filter will be explained below in relationto a scenario in which there are only four input samples and the X_(n-k)values are all initialized to zero values in the filter memory (notshown). This scenario is selected for ease and simplicity of discussion.

During operation, four input samples X0, X1, X2 and X3 are input intothe polyphase filter, and sixteen samples Y0, Y1, Y2, . . . , Y15 areoutput from the polyphase filter. Operations of the first polyphasefilter bank 902 are defined by the following Mathematical Equations(1)-(4).Y0=X0*C0  (1)Y1=X0*C4+X1*C0  (2)Y2=X0*C8+X1*C4+X2*C0  (3)Y3=X0*C12+X1*C8+X2*C4+X3*C0  (4)Operations of the second polyphase filter bank 904 are defined by thefollowing Mathematical Equations (5)-(8).Y1=X0*C1  (5)Y5=X0*C5+X1*C1  (6)Y9=X0*C9+X1*C5+X2*C1  (7)Y13=X0*C13+X1*C9+X2*C5+X3*C1  (8)Operations of the third polyphase filter bank 906 are defined by thefollowing Mathematical Equations (9)-(12).Y2=X0*C2  (9)Y6=X0*C6+X1*C2  (10)Y10=X0*C10+X1*C6+X2*C2Y14=X0*C14+X1*C10+X2*C6+X3*C2  (12)Operations of the second polyphase filter bank 908 are defined by thefollowing Mathematical Equations (13)-(16).Y2=X0*C3  (13)Y6=X0*C7+X1*C3  (14)Y10=X0*C11+X1*C7+X2*C3  (15)Y14=X0*C15+X1*C11+X2*C7+X3*C3  (16)As evident from Mathematical Equations (1)-(16), for four input valuesX0, X1, X2 and X3, sixteen values are output Y0, Y2, . . . , Y15.

Referring now to FIG. 10, there is provided an illustration that isuseful for understanding how the 4:1 interpolator of FIG. 9 istransformed into a 1:1 interpolator with decimation. Similar to FIG. 9,the operations of this 1:1 interpolator with decimation will beexplained below in relation to a scenario in which there are only fourinput samples and the X_(n-k) values are all initialized to zero valuesin the filter memory (not shown). This scenario is selected for ease andsimplicity of discussion.

When decimation is employed, output samples are selectively discarded sothat for every one sample in, there is only one sample out. For example,if samples X0-X4 are input into the polyphase filter, then samples Y0,Y4, Y8, Y12 are output from the polyphase filter since Y0 is where X0first appears, Y4 is where X1 first appears, Y8 is where X3 firstappears and Y12 is where X4 first appears. With an optimized polyphaseresampler, the samples which are to be discarded are not calculated.

Referring now to FIG. 11, there is provided an illustration that isuseful for understanding how the polyphase filter is used in accordancewith the present solution. As noted above, the present solution isdesigned to introduce time advancements in a sequence of sample and/ortime retardations in a sequence of samples using a polyphase filter. Atime advancement results in an output sample (e.g., output sample Z2)having a relatively shorter duration. In contrast, a time retardationresults in an output sample (e.g., output sample Z2) having a relativelylonger duration. The manner in which time advancements and timeretardations are achieved will now be discussed in relation to FIG. 12and FIG. 13.

Referring now to FIG. 12, time advancements will be discussed inrelation to a scenario where: (1) four polyphase filter banks 802-808are employed, each with four coefficients assigned thereto; and (2)there are only four input samples and the X_(n-k) values are allinitialized to zero values in the filter memory (not shown). In thisscenario, a first polyphase filter bank 802 is configured to computefour outputs Y0, Y4, Y8, Y12 when a sample sequence X0-X4 is inputthereto. A second polyphase filter bank 804 is configured to computefour outputs Y1, Y5, Y9, Y13 when a sample sequence X0-X4 is inputthereto. A third polyphase filter bank 806 is configured to compute fouroutputs Y2, Y6, Y10, Y14 when a sample sequence X0-X4 is input thereto.A fourth polyphase filter bank 806 is configured to compute four outputsY3, Y7, Y11, Y15 when a sample sequence X0-X4 is input thereto. In orderto make a time advancement having a value less than a sample duration,output samples for all but one polyphase filter bank are discarded(e.g., via decimator 810 of FIG. 8). In order to introduce a time delayhaving a value equal to a sample duration, a sample is dropped from theoutput sequence (e.g., drop Z0 from the output sequence Z0-Z4).

As shown in FIG. 12A, a relative time advance equal to a quarter (0.25)of a sample duration is achieved by selecting the outputs of the secondpolyphase filter bank 804, and discarding the outputs of the otherpolyphase filter banks 802, 806, 808. In this case, the output of thepolyphase resampling filter operations 704 of FIG. 7 comprises Z0-Z3defined by the following Mathematical Equations (17)-(20).Z0=X0*C1  (17)Z1=X0*C5+X1*C1  (18)Z2=X0*C9+X1*C5+X2*C1  (19)Z3=X0*C13+X1*C9+X2*C5+X3*C1  (20)The first output sample Z0 has a sample duration that is 0.25 of asample duration shorter than the other output samples Z1-Z3. In effect,samples Z1-Z3 appear earlier in the transmit sequence of samples.

As shown in FIG. 12B, a relative time advance equal to a half (0.50) ofa sample duration is achieved by selecting the outputs of the thirdpolyphase filter bank 806, and discarding the outputs of the otherpolyphase filter banks 802, 804, 808. In this case, the output of thepolyphase resampling filter operations 704 of FIG. 7 comprises Z0-Z3defined by the following Mathematical Equations (21)-(24).Z0=X0*C2  (21)Z1=X0*C6+X1*C2  (22)Z2=X0*C10+X1*C6+X2*C2  (23)Z3=X0*C14+X1*C10+X2*C6+X3*C2  (24)The first output sample Z0 has a sample duration that is 0.50 of asample duration shorter than the other output samples Z1-Z3. In effect,samples Z1-Z3 appear earlier in the transmit sequence of samples.

As shown in FIG. 12C, a relative time advance equal to three quarters(0.75) of a sample duration is achieved by selecting the outputs of thefourth polyphase filter bank 808, and discarding the outputs of theother polyphase filter banks 802, 804, 806. In this case, the output ofthe polyphase resampling filter operations 704 of FIG. 7 comprises Z0-Z3defined by the following Mathematical Equations (25)-(28).Z0=X0*C3  (25)Z1=X0*C7+X1*C3  (26)Z2=X0*C11+X1*C7+X2*C3  (27)Z3=X0*C15+X1*C11+X2*C7+X3*C3  (28)The first output sample Z0 has a sample duration that is 0.75 of asample duration shorter than the other output samples Z1-Z3. In effect,samples Z1-Z3 appear earlier in the transmit sequence of samples.

As shown in FIG. 12D, a relative time advance equal to one (1.00) sampleduration is achieved by selecting the outputs of the first polyphasefilter bank 802, and discarding (A) the outputs of the other polyphasefilter banks 804, 806, 808 and (B) the first output of the firstpolyphase filter bank 802. In this case, the output of the polyphaseresampling filter operations 704 of FIG. 7 comprises Z1-Z3 defined bythe following Mathematical Equations (29)-(30).Z1=X0*C4+X1*C0  (29)Z2=X0*C8+X1*C4+X2*C0  (20)Z3=X0*C12+X1*C8+X2*C4+X3*C0  (30)In effect, samples Z1-Z3 appear earlier in the transmit sequence by afull sample duration.

Referring now to FIG. 13, time retardations will be discussed inrelation to a scenario where: (1) four polyphase filter banks 802-808are employed, each with four coefficients assigned thereto; and (2)there are only four input samples and the X_(n-k) values are allinitialized to zero values in the filter memory (not shown).

As shown in FIG. 13A, a relative time retardation equal to a quarter(0.25) of a sample duration is achieved by selecting the outputs of thefirst and second polyphase filter banks 802, 804, and discarding (A) theoutputs of the other polyphase filter banks 806, 808, (B) the second,third and fourth outputs of the first polyphase filter bank 802, and (C)the first output of the second polyphase filter banks 804. In this case,the output of the polyphase resampling filter operations 704 of FIG. 7comprises Z0-Z3 defined by the following Mathematical Equations(31)-(34).Z0=X0*C0  (31)Z1=X0*C5+X1*C1  (32)Z2=X0*C9+X1*C5+X2*C1  (33)Z3=X0*C13+X1*C9+X2*C5+X3*C1  (34)The first output sample Z0 has a 0.25 longer sample duration than thatof the other output samples Z1-Z3. In effect, samples Z1-Z3 appear laterin the transmit sequence of samples.

As shown in FIG. 13B, a relative time retardation equal to a half (0.50)of a sample duration is achieved by selecting the outputs of the firstand third polyphase filter banks 802, 806, and discarding (A) theoutputs of the other polyphase filter banks 804, 808, (B) the second,third and fourth outputs of the first polyphase filter bank 802, and (C)the first output of the third polyphase filter banks 806. In this case,the output of the polyphase resampling filter operations 704 of FIG. 7comprises Z0-Z3 defined by the following Mathematical Equations(35)-(38).Z0=X0*C0  (35)Z1=X0*C6+X1*C2  (36)Z2=X0*C10+X1*C6+X2*C2  (37)Z3=X0*C14+X1*C10+X2*C6+X3*C2  (38)The first output sample Z0 has a 0.50 longer sample duration than thatof the other output samples Z1-Z3. In effect, samples Z1-Z3 appear laterin the transmit sequence of samples.

As shown in FIG. 13C, a relative time retardation equal to threequarters (0.75) of a sample duration is achieved by selecting theoutputs of the first and fourth polyphase filter banks 802, 808, anddiscarding (A) the outputs of the other polyphase filter banks 804, 806,(B) the second, third and fourth outputs of the first polyphase filterbank 802, and (C) the first output of the fourth polyphase filter banks808. In this case, the output of the polyphase resampling filteroperations 704 of FIG. 7 comprises Z0-Z3 defined by the followingMathematical Equations (39)-(42).Z0=X0*C0  (39)Z1=X0*C7+X1*C3  (40)Z2=X0*C11+X1*C7+X2*C3  (41)Z3=X0*C15+X1*C11+X2*C7+X3*C3  (42)The first output sample Z0 has a 0.75 longer sample duration than thatof the other output samples Z1-Z3. In effect, samples Z1-Z3 appear laterin the transmit sequence of samples.

In most applications of the present solution, the input sequencecomprises N samples X0, X1, . . . , XN, where N is any integer greaterthan zero. One or more time advancements and/or time retardations can beadded to the sequence of samples via the polyphase resampling filteroperations 704. The value of each time advancement/retardation can berandomly selected. In the case that more than one time advancement orretardation is made, the values thereof can be selected so that they aredifferent throughout the entire sequence of samples (e.g., 128 samples)or only in a portion of the sequence of samples (e.g., 64 samples).Also, the number of samples S between time advancements and/orretardations can be the same or different. In the case where the numberof samples between time advancements and/or retardations is different, Shas a variable value which may be randomly selected. Further, theabove-described process can be optimized by selectively computing onlythose values which are to be output as samples Z0-ZN (i.e., nodiscarding operations are performed). The result from performing thepresent solution is an elimination or reduction of cyclostationaryfeatures in a transmitted waveform.

Referring now to FIG. 14, there is provided a more detailed blockdiagram of the receiver 406 shown in FIG. 4. Receiver 406 illustratesthe removal of time advancements and/or time retardations from thereceive side and the recovery of the transmitted signal. As such,receiver 406 is comprised of an antenna 1402, an RF-to-IF converter1404, an Analog-to-Digital Converter (“ADC”) 1406, a sub-sample ditherremoval device 1410, an optional symbol de-spreader 1412, and a symboldemodulator 1414.

Antenna 1402 is configured to receive signals transmitted fromtransmitter 404. Antenna 1402 is also configured to communicate receivedsignals to RF-to-IF converter 1404. RF-to-IF converter 1404 isconfigured to translate in frequency a relatively high-frequency RFsignal to a different frequency IF signal. Apparatus and methods forperforming RF-to-IF conversions are well known in the art, and thereforewill not be described herein. Any known or to be known apparatus ormethod for performing RF-to-IF conversions can be used herein.

The output of the RF-to-IF converter 1404 is passed to the input of theADC 1406. ADC 1406 is configured to convert analog voltage values todigital values, and communicate the digital values to the sub-sampledither removal device 1410.

The sub-sample dither removal device 1410 is generally configured toperform the inverse of the polyphase resampling filter operations 704 ofthe transmitter 404, and present a sequence of samples absent of anytime advancements and/or time retardations to the following component(s)1412, 1414. An illustrative architecture of the sub-sample ditherremoval device 1410 is provided in FIG. 15. FIG. 15 will be discussedbelow. The output of the sub-sample dither removal device 1410 isprovided to subsequent devices 1412, 1414 in the receiver 406. Thesedevices include an optional symbol de-spreader and a symbol demodulator.Symbol de-spreader and demodulators are well known in the art, andtherefore will not be described herein.

Referring now to FIG. 15, there is provided a detailed block diagram ofan illustrative architecture for the sub-sample dither removal device1410. Device 1410 may include more or less components than those shownin FIG. 15. However, the components shown are sufficient to disclose anillustrative embodiment implementing the present solution. The hardwarearchitecture of FIG. 15 represents one embodiment of a representativesub-sample dither removal device configured to facilitatecyclostationary feature elimination. As such, the device 1410 of FIG. 15implements at least a portion of a method for selectively removing timeadvances and/or delays in a sequence of samples in accordance with thepresent solution.

Some or all components of the device 1410 can be implemented ashardware, software and/or a combination of hardware and software. Thehardware includes, but is not limited to, one or more electroniccircuits. The electronic circuits can include, but are not limited to,passive components (e.g., resistors and capacitors) and/or activecomponents (e.g., amplifiers and/or microprocessors). The passive and/oractive components can be adapted to, arranged to and/or programmed toperform one or more of the methodologies, procedures, or functionsdescribed herein.

As shown in FIG. 15, the device 1410 comprises an input port 1502, aprocessing unit 1506, an output port 1504, a system bus 1510, a randomnumber generator 1516, a memory 1512 connected to and accessible byother portions of device 1410 through system bus 1510, and hardwareentities 1514 connected to system bus 1510.

At least some of the hardware entities 1514 perform actions involvingaccess to and use of memory 1512. Hardware entities 1514 can include acomputer-readable storage medium 1518 on which is stored one or moresets of instructions 1520 (e.g., software code) configured to implementone or more of the methodologies, procedures, or functions describedherein. The instructions 1520 can also reside, completely or at leastpartially, within the memory 1512 and/or within the processing unit 1506during execution thereof by the device 1410. The memory 1512 and theprocessing unit 1506 also can constitute machine-readable media. Theterm “machine-readable media”, as used here, refers to a single mediumor multiple media that store the one or more sets of instructions 1520.The term “machine-readable media”, as used here, also refers to anymedium that is capable of storing, encoding or carrying a set ofinstructions 1520 for execution by the device 1410 and that cause thedevice 1410 to perform any one or more of the methodologies of thepresent disclosure.

Referring now to FIGS. 16-17, there are provided illustrations that areuseful for understanding the operations performed by the sub-sampledither removal device 1410. The operations include polyphase desamplingfilter operations 1604 for selectively removing time advances and/ortime retardations (or delays) in a received sequence of samples Z0, Z1,Z2, . . . , Z11. The output of the polyphase desampling filteroperations 1604 is referred to herein as a sequence of samples W0, W1,W2, . . . , W11. Notably, the polyphase desampling filter operations1604 outputs the same number of samples as it receives, i.e., there is a1 to 1 correspondence between input samples and output samples. Althoughthe sequence of samples is shown in FIG. 16 as comprising twelvesamples, the present solution is not limited in this regard. Thesequence of samples can comprise any number of samples in accordancewith a given application.

The time advances/retardations are removed using a plurality ofpolyphase filter banks 1702, 1704, 1706, 1708 so that all samples outputfrom the sub-sample dither removal device 1410 have the same duration.Polyphase filter banks are well known in the art, and therefore will notbe described here in detail. Although four polyphase filter banks areshown in FIG. 17, the present solution is not limited in this regard.Any number of polyphase filter banks can be employed herein inaccordance with a particular application. In some scenarios, 128polyphase filter banks are provided, each with 12 coefficients, so thattime advances and delays which are multiples of 1/128 of a sampleduration can be chosen. The present solution is not limited in thisregard.

Referring now to FIG. 18, there is an illustration showing the resultsfrom computations performed by the polyphase filter banks 1702, 1704,1706, 1708. Each filter bank has four coefficients assigned thereto.More specifically, a first polyphase filter bank 1702 has coefficientsC0, C4, C8 and C12 assigned thereto. A second polyphase filter bank 1704has coefficients C1, C5, C9 and C13 assigned thereto. A third polyphasefilter bank 1706 has coefficients C2, C6, C10 and C14 assigned thereto.A fourth polyphase filter bank 1708 has coefficients C3, C7, C11 and C15assigned thereto.

Operation of this polyphase filter will be explained below in relationto a scenario in which there are only four input samples Z_(n-k) and theZ_(n-k) values are all initialized to zero values in the filter memory(not shown). This scenario is selected for ease and simplicity ofdiscussion.

During operation, four input samples Z0, Z1, Z2 and Z3 are input intothe polyphase filter. Operations of the first polyphase filter bank 1702are defined by the following Mathematical Equations (43)-(46).Q0=Z0*C0  (43)Q1=Z0*C4+Z1*C0  (44)Q2=Z0*C8+Z1*C4+Z2*C0  (45)Q3=Z0*C12+Z1*C8+Z2*C4+Z3*C0  (46)Operations of the second polyphase filter bank 1704 are defined by thefollowing Mathematical Equations (47)-(50).Q1=Z0*C1  (47)Q5=Z0*C5+Z1*C1  (48)Q9=Z0*C9+Z1*C5+Z2*C1  (49)Q13=Z0*C13+Z1*C9+Z2*C5+Z3*C1  (50)Operations of the third polyphase filter bank 1706 are defined by thefollowing Mathematical Equations (51)-(54).Q2=Z0*C2  (51)Q6=Z0*C6+Z1*C2  (52)Q10=Z0*C10+Z1*C6+Z2*C2  (53)Q14=Z0*C14+Z1*C10+Z2*C6+Z3*C2  (54)Operations of the second polyphase filter bank 1708 are defined by thefollowing Mathematical Equations (55)-(58).Q2=Z0*C3  (55)Q6=Z0*C7+Z1*C3  (56)Q10=Z0*C11+Z1*C7+Z2*C3  (57)Q14=Z0*C15+Z1*C11+Z2*C7+Z3*C3  (58)As evident from Mathematical Equations (43)-(58), for four input valuesZ0, Z1, X2 and Z3, there are sixteen resulting values Q0, Q2, . . . ,Q15. In some scenarios, all sixteen resulting values are computed. Inother scenarios, only select ones of the sixteen resulting values arecomputed.

Referring now to FIG. 19, there is provided illustrations that areuseful for understanding how the polyphase filter 1700 is used inaccordance with the present solution. As noted above, the presentsolution is designed to introduce time advancements in a sequence ofsample and/or time retardations in a sequence of samples using apolyphase filter at the transmit side. The inverse of these transmitside polyphase filter operations are performed at the receive side. Inthis regard, the polyphase filter 1700 is used at the receive side toremove time advancements and/or time retardations from a receivedsequence of samples. The manner in which time advancements are removedwill now be discussed in relation to FIG. 19. The manner in which timeretardations are removed are discussed below in relation to FIG. 20.

Referring now to FIG. 19, time advancements will be discussed inrelation to a scenario where: (1) four polyphase filter banks 1702-1708are employed, each with four coefficients assigned thereto; and (2)there are only four input samples and the Z_(n-k) values are allinitialized to zero values in the filter memory (not shown).

Referring now to FIG. 19A, a relative time advancement equal to aquarter (0.25) of a sample duration is removed by performing a timeretardation equal to quarter (0.25) of a sample duration. Such a timeretardation is achieved by selecting the outputs of the first and secondpolyphase filter banks 1702, 1704, and discarding (A) the outputs of theother polyphase filter banks 1706, 1708, (B) the second, third andfourth outputs of the first polyphase filter bank 1702, and (C) thefirst output of the second polyphase filter banks 1704. In this case,the output of the polyphase resampling filter operations 1604 of FIG. 16comprises W0-W3 defined by the following Mathematical Equations(59)-(62).W0=Z0*C0  (59)W1=Z0*C5+Z1*C1  (60)W2=Z0*C9+Z1*C5+Z2*C1  (61)W3=Z0*C13+Z1*C9+Z2*C5+Z3*C1  (62)The first output sample W0 has a 0.25 longer sample duration than thatof the corresponding input sample Z0, i.e., the 0.25 time advancementhas been removed. In effect, all of the output samples W0-W3 have thesame sample duration.

As shown in FIG. 19B, a relative time advancement equal to a half (0.50)of a sample duration is removed by performing a time retardation equalto a half (0.50) of a sample duration. Such a time retardation isachieved by selecting the outputs of the first and third polyphasefilter banks 1702, 1706, and discarding (A) the outputs of the otherpolyphase filter banks 1704, 1708, (B) the second, third and fourthoutputs of the first polyphase filter bank 1702, and (C) the firstoutput of the third polyphase filter banks 1706. In this case, theoutput of the polyphase resampling filter operations 1604 of FIG. 16comprises Z0-Z3 defined by the following Mathematical Equations(63)-(66).W0=Z0*C0  (63)W1=Z0*C6+Z1*C2  (64)W2=Z0*C10+Z1*C6+Z2*C2  (65)W3=Z0*C14+Z1*C10+Z2*C6+Z3*C2  (66)The first output sample W0 has a 0.50 longer sample duration than thatof the corresponding input sample Z0, i.e., the 0.50 time advancementhas been removed. In effect, samples W0-W3 have the same sampleduration.

As shown in FIG. 19C, a relative time advancement equal to threequarters (0.75) of a sample duration is removed by performing a timeretardation equal to three quarters (0.75) of a sample duration. Such atime retardation is achieved by selecting the outputs of the first andfourth polyphase filter banks 1702, 1708, and discarding (A) the outputsof the other polyphase filter banks 1704, 1706, (B) the second, thirdand fourth outputs of the first polyphase filter bank 1702, and (C) thefirst output of the fourth polyphase filter banks 1708. In this case,the output of the polyphase resampling filter operations 1604 of FIG. 16comprises W0-W3 defined by the following Mathematical Equations(67)-(70).W0=Z0*C0  (67)W1=Z0*C7+Z1*C3  (68)W2=Z0*C11+Z1*C7+Z2*C3  (69)W3=Z0*C15+Z1*C11+Z2*C7+Z3*C3  (70)The first output sample W0 has a 0.75 longer sample duration than thatof the corresponding input sample Z0, i.e., the 0.75 time advancementhas been removed. In effect, samples W0-W3 have the same sampleduration.

Referring now to FIG. 19D, a relative time advancement equal to one(1.00) sample duration is removed by performing a time retardation equalto one (1.00) sample duration. Such a time retardation is achieved byperforming first polyphase filter bank computations and repeating aprevious sample. In this case, the output of the polyphase resamplingfilter operations 1604 of FIG. 16 comprises W0-W3 defined by thefollowing Mathematical Equations (71)-(74).W0=Z0*C0  (71)W1=Z0*C4+Z1*C0  (72)W2=Z0*C8+Z1*C4+Z2*C0  (73)W3=Z0*C12+Z1*C8+Z2*C4+Z3*C0  (74)The output samples W1-W3 are shifted in time by one sample duration. Asample output immediately prior to W1 is repeated as shown by Wrepeat.

Referring now to FIG. 20, time retardations will be discussed inrelation to a scenario where: (1) four polyphase filter banks 1702-1708are employed, each with four coefficients assigned thereto; and (2)there are only four input samples and the Z_(n-k) values are allinitialized to zero values in the filter memory (not shown).

Referring now to FIG. 20A, a relative time retardation equal to 0.25 ofa sample duration is removed by performing a time advancement equal to0.25 of a sample duration. A time advance equal to a quarter (0.25) of asample duration is achieved by selecting the outputs of the secondpolyphase filter bank 1704, and discarding the outputs of the otherpolyphase filter banks 1702, 1706, 1708. In this case, the output of thepolyphase resampling filter operations 1604 of FIG. 16 comprises W1-W3defined by the following Mathematical Equations (75)-(78).W0=Z0*C1  (75)W1=Z0*C5+Z1*C1  (76)W2=Z0*C9+Z1*C5+Z2*C1  (77)W3=Z0*C13+Z1*C9+Z2*C5+Z3*C1  (78)The first output sample W0 has a 0.25 shorter sample duration than thatof the corresponding input sample Z0, i.e., the 0.25 time retardationhas been removed. In effect, samples W0-W3 have the same sampleduration.

Referring now to FIG. 20B, a relative time retardation equal to 0.50 ofa sample duration is removed by performing a time advancement equal to0.50 of a sample duration. A time advance equal to a half (0.50) of asample duration is achieved by selecting the outputs of the thirdpolyphase filter bank 1706, and discarding the outputs of the otherpolyphase filter banks 1702, 1704, 1708. In this case, the output of thepolyphase resampling filter operations 1604 of FIG. 16 comprises W1-W3defined by the following Mathematical Equations (79)-(82).W0=Z0*C2  (79)W1=Z0*C6+Z1*C2  (80)W2=Z0*C10+Z1*C6+Z2*C2  (81)W3=Z0*C14+Z1*C10+Z2*C6+Z3*C2  (82)The first output sample W0 has a 0.50 shorter sample duration than thatof the corresponding input sample Z0, i.e., the 0.50 time retardationhas been removed. In effect, samples W0-W3 have the same sampleduration.

Referring now to FIG. 20C, a relative time retardation equal to 0.75 ofa sample duration is removed by performing a time advancement equal to0.75 of a sample duration. A time advance equal to three quarters (0.75)of a sample duration is achieved by selecting the outputs of the fourthpolyphase filter bank 1708, and discarding the outputs of the otherpolyphase filter banks 1702, 1704, 1706. In this case, the output of thepolyphase resampling filter operations 1604 of FIG. 16 comprises W1-W3defined by the following Mathematical Equations (83)-(86).W0=Z0*C3  (83)W1=Z0*C7+Z1*C3  (84)W2=Z0*C11+Z1*C7+Z2*C3  (85)W3=Z0*C15+Z1*C11+Z2*C7+Z3*C3  (86)The first output sample W0 has a 0.75 shorter sample duration than thatof the corresponding input sample Z0, i.e., the 0.75 time retardationhas been removed. In effect, samples W0-W3 have the same sampleduration.

Referring now to FIG. 21, there is provided a graph that is useful forunderstanding the present solution. A polyphase resampler at thereceiver will line up the impulse response (at the receiver) so that thedemodulation will appear stationary in time. This is accomplished whenthe transmitter timing is advanced (for example) and the receiver timingis retarded by the exact same amount. If a 128 bank resampler is used(for example) a transmit choice of tap 32 will lead to a receive offsetof tap 96.

Since the polyphase filter banks are not the same, a perfect matchedfilter is not provided at the receiver as shown by FIG. 21. If thetransmitter selected polyphase filter bank one, then the receiver willuse polyphase filter bank three to inverse the polyphase filteroperations performed at the transmitter. The coefficients of the firstand third polyphase filter banks are different. Therefore, the samplevalue generated at the receiver is different than the sample valuegenerated at the transmitter, but the delay lines up. In effect, the BitError Rate (“BER”) is not perfectly recovered.

Referring now to FIG. 22, there is provided another graph showing theslight degradation of the BER for a communications system implementingthe present solution. Line 2200 shows the BER for a system employing astandard uncoded orthogonal communications scheme (i.e., no ditheringperformed). Line 2202 shows the BER for a system employing an techniquein which a perfectly matched filter is employed by the transmitter andreceiver. Line 2204 shows the BER for a system implementing the presentsolution. As evident from lines 2202 and 2204, there is a 0.25 dBdegradation of the BER in the system implementing the present solutionas compared to the system having a perfectly matched filter.

All of the apparatus, methods, and algorithms disclosed and claimedherein can be made and executed without undue experimentation in lightof the present disclosure. While the invention has been described interms of preferred embodiments, it will be apparent to those havingordinary skill in the art that variations may be applied to theapparatus, methods and sequence of steps of the method without departingfrom the concept, spirit and scope of the invention. More specifically,it will be apparent that certain components may be added to, combinedwith, or substituted for the components described herein while the sameor similar results would be achieved. All such similar substitutes andmodifications apparent to those having ordinary skill in the art aredeemed to be within the spirit, scope and concept of the invention asdefined.

The features and functions disclosed above, as well as alternatives, maybe combined into many other different systems or applications. Variouspresently unforeseen or unanticipated alternatives, modifications,variations or improvements may be made by those skilled in the art, eachof which is also intended to be encompassed by the disclosedembodiments.

We claim:
 1. A method for removing dither introduced into a transmittedradio frequency (RF) signal, comprising: receiving, by a receiver, thetransmitted RF signal; converting, by the receiver, the transmitted RFsignal into a discrete-time intermediate frequency (IF) signalcomprising a sequence of samples, where at least a first sample of saidsamples has a first sample duration different than a second sampleduration of at least a second sample of said samples; and performingoperations by a sub-sample dither removal device of the receiver tomodify a sample timing of the discrete-time IF signal by decreasing orincreasing the first sample duration of the first sample using a digitalsignal processing technique in a digital domain; wherein the firstsample duration of the first sample is increased or decreased by a firstamount different than a second amount by which a third sample of saidsamples duration of a third sample is increased or decreased.
 2. Themethod according to claim 1, wherein the digital signal processingtechnique comprises a polyphase resampling filter technique, a sampledropping/repeating technique, or a Farrow filter technique that adds ordrops a plurality of samples from the discrete-time IF signal.
 3. Amethod for removing dither introduced into a transmitted radio frequency(RF) signal, comprising: receiving, by a receiver, the transmitted RFsignal; converting, by the receiver, the transmitted RF signal into adiscrete-time intermediate frequency (IF) signal comprising a sequenceof samples, where at least a first sample of said samples has a firstsample duration different than a second sample duration of at least asecond sample of said samples; and performing operations by a sub-sampledither removal device of the receiver to modify a sample timing of thediscrete-time IF signal by decreasing or increasing the first sampleduration of the first sample using a digital signal processing techniquein a digital domain; wherein: the first sample duration of the firstsample is longer than the second sample duration of the second sample;and the first sample duration is decreased by a first incremental amountof a sample duration by outputting results only from a first select oneof a plurality of polyphase filter banks from the sub-sample ditherremoval device.
 4. The method according to claim 3, wherein results fromall unselected ones of the poyphase filter banks are discarded or notcomputed.
 5. The method according to claim 3, wherein the duration of atleast one third sample of the sequence is decreased by a secondincremental amount of the sample duration by outputting results onlyfrom a second select one of the plurality of polyphase filter banks fromthe sub-sample dither removal device.
 6. A method for removing ditherintroduced into a transmitted radio frequency (RF) signal, comprising:receiving, by a receiver, the transmitted RF signal; converting, by thereceiver, the transmitted RF signal into a discrete-time intermediatefrequency (IF) signal comprising a sequence of samples, where at least afirst sample of said samples has a first sample duration different thana second sample duration of at least a second sample of said samples;and performing operations by a sub-sample dither removal device of thereceiver to modify a sample timing of the discrete-time IF signal bydecreasing or increasing the first sample duration of the first sampleusing a digital signal processing technique in a digital domain;wherein: the first sample duration of the first sample is shorter thanthe second sample duration of the second sample; and the first sampleduration is increased by a first incremental amount of a sample durationby outputting only one result from a first select one of a plurality ofpolyphase filter banks of the sub-sample dither removal device,immediately followed by at least one result from a second differentselect one of the plurality of polyphase filter banks.
 7. The methodaccording to claim 6, wherein the duration of at least one third sampleof the sequence is increased by a second incremental amount of thesample duration by outputting only one result from the first select oneof a plurality of polyphase filter banks of the sub-sample ditherremoval device, immediately followed by at least one result from a thirddifferent select one of the plurality of polyphase filter banks.
 8. Amethod for removing dither introduced into a transmitted radio frequency(RF) signal, comprising: receiving, by a receiver, the transmitted RFsignal; converting, by the receiver, the transmitted RF signal into adiscrete-time intermediate frequency (IF) signal comprising a sequenceof samples, where at least a first sample of said samples has a firstsample duration different than a second sample duration of at least asecond sample of said samples; and performing operations by a sub-sampledither removal device of the receiver to modify a sample timing of thediscrete-time IF signal by decreasing or increasing the first sampleduration of the first sample using a digital signal processing techniquein a digital domain; wherein a time advance equal to one sample durationis removed from the discrete-time IF signal at the sub-sample ditherremoval device by repeating a sample in a sequence of output samples. 9.A method for removing dither introduced into a transmitted radiofrequency (RF) signal, comprising: receiving, by a receiver, thetransmitted RF signal; converting, by the receiver, the transmitted RFsignal into a discrete-time intermediate frequency (IF) signalcomprising a sequence of samples, where at least a first sample of saidsamples has a first sample duration different than a second sampleduration of at least a second sample of said samples; and performingoperations by a sub-sample dither removal device of the receiver tomodify a sample timing of the discrete-time IF signal by decreasing orincreasing the first sample duration of the first sample using a digitalsignal processing technique in a digital domain; wherein a time advanceequal to an amount of a sample duration is removed from thediscrete-time IF signal at the sub-sample dither removal device byintroducing a time retardation equal to the amount of the sampleduration into the discrete-time IF signal.
 10. A method for removingdither introduced into a transmitted radio frequency (RF) signal,comprising: receiving, by a receiver, the transmitted RF signal;converting, by the receiver, the transmitted RF signal into adiscrete-time intermediate frequency (IF) signal comprising a sequenceof samples, where at least a first sample of said samples has a firstsample duration different than a second sample duration of at least asecond sample of said samples; and performing operations by a sub-sampledither removal device of the receiver to modify a sample timing of thediscrete-time IF signal by decreasing or increasing the first sampleduration of the first sample using a digital signal processing techniquein a digital domain; wherein a time retardation equal to an amount of asample duration is removed from the discrete-time IF signal at thesub-sample dither removal device by introducing a time advancement equalto the amount of the sample duration into the discrete-time IF signal.11. A receiver, comprising: an antenna configured to receive atransmitted radio frequency (RF) signal into which dither has beenintroduced; a converter configured to convert the transmitted RF signalinto a discrete-time intermediate frequency (IF) signal comprising asequence of samples, where at least a first sample of said samples has afirst sample duration different than a second sample duration of atleast a second sample of said samples; and a sub-sample dither removaldevice configured to perform operations to modify a sample timing of thediscrete-time IF signal by decreasing or increasing the first sampleduration of the first sample using a digital signal processing techniquein a digital domain; wherein the first sample duration of the firstsample is increased or decreased by a first amount different than asecond amount by which a third sample of said samples duration of athird sample is increased or decreased.
 12. The receiver according toclaim 11, wherein the digital signal processing technique comprises apolyphase resampling filter technique, a sample dropping/repeatingtechnique, or a Farrow filter technique that adds or drops a pluralityof samples from the discrete-time IF signal.
 13. A receiver, comprising:an antenna configured to receive a transmitted radio frequency (RF)signal into which dither has been introduced; a converter configured toconvert the transmitted RF signal into a discrete-time intermediatefrequency (IF) signal comprising a sequence of samples, where at least afirst sample of said samples has a first sample duration different thana second sample duration of at least a second sample of said samples;and a sub-sample dither removal device configured to perform operationsto modify a sample timing of the discrete-time IF signal by decreasingor increasing the first sample duration of the first sample using adigital signal processing technique in a digital domain; wherein: thefirst sample duration of the first sample is longer than the secondsample duration of the second sample; and the first sample duration isdecreased by a first incremental amount of a sample duration byoutputting results only from a first select one of a plurality ofpolyphase filter banks from the sub-sample dither removal device. 14.The receiver according to claim 13, wherein results from all unselectedones of the poyphase filter banks are discarded or not computed.
 15. Thereceiver according to claim 13, wherein the duration of at least onethird sample of the sequence is decreased by a second incremental amountof the sample duration by outputting results only from a second selectone of the plurality of polyphase filter banks from the sub-sampledither removal device.
 16. A receiver, comprising: an antenna configuredto receive a transmitted radio frequency (RF) signal into which ditherhas been introduced; a converter configured to convert the transmittedRF signal into a discrete-time intermediate frequency (IF) signalcomprising a sequence of samples, where at least a first sample of saidsamples has a first sample duration different than a second sampleduration of at least a second sample of said samples; and a sub-sampledither removal device configured to perform operations to modify asample timing of the discrete-time IF signal by decreasing or increasingthe first sample duration of the first sample using a digital signalprocessing technique in a digital domain; wherein: the first sampleduration of the first sample is shorter than the second sample durationof the second sample; and the first sample duration is increased by afirst incremental amount of a sample duration by outputting only oneresult from a first select one of a plurality of polyphase filter banksof the sub-sample dither removal device, immediately followed by atleast one result from a second different select one of the plurality ofpolyphase filter banks.
 17. The receiver according to claim 16, whereinthe duration of at least one third sample of the sequence is increasedby a second incremental amount of the sample duration by outputting onlyone result from the first select one of a plurality of polyphase filterbanks of the sub-sample dither removal device, immediately followed byat least one result from a third different select one of the pluralityof polyphase filter banks.
 18. A receiver, comprising: an antennaconfigured to receive a transmitted radio frequency (RF) signal intowhich dither has been introduced; a converter configured to convert thetransmitted RF signal into a discrete-time intermediate frequency (IF)signal comprising a sequence of samples, where at least a first sampleof said samples has a first sample duration different than a secondsample duration of at least a second sample of said samples; and asub-sample dither removal device configured to perform operations tomodify a sample timing of the discrete-time IF signal by decreasing orincreasing the first sample duration of the first sample using a digitalsignal processing technique in a digital domain; wherein a time advanceequal to one sample duration is removed from the discrete-time IF signalat the sub-sample dither removal device by repeating a sample in asequence of output samples.
 19. A receiver, comprising: an antennaconfigured to receive a transmitted radio frequency (RF) signal intowhich dither has been introduced; a converter configured to convert thetransmitted RF signal into a discrete-time intermediate frequency (IF)signal comprising a sequence of samples, where at least a first sampleof said samples has a first sample duration different than a secondsample duration of at least a second sample of said samples; and asub-sample dither removal device configured to perform operations tomodify a sample timing of the discrete-time IF signal by decreasing orincreasing the first sample duration of the first sample using a digitalsignal processing technique in a digital domain; wherein a time advanceequal to an amount of a sample duration is removed from thediscrete-time IF signal at the sub-sample dither removal device byintroducing a time retardation equal to the amount of the sampleduration into the discrete-time IF signal.
 20. A receiver, comprising:an antenna configured to receive a transmitted radio frequency (RF)signal into which dither has been introduced; a converter configured toconvert the transmitted RF signal into a discrete-time intermediatefrequency (IF) signal comprising a sequence of samples, where at least afirst sample of said samples has a first sample duration different thana second sample duration of at least a second sample of said samples;and a sub-sample dither removal device configured to perform operationsto modify a sample timing of the discrete-time IF signal by decreasingor increasing the first sample duration of the first sample using adigital signal processing technique in a digital domain; wherein a timeretardation equal to an amount of a sample duration is removed from thediscrete-time IF signal at the sub-sample dither removal device byintroducing a time advancement equal to the amount of the sampleduration into the discrete-time IF signal.